After workpieces have been produced, it is common practice to inspect them on a coordinate positioning apparatus, such as a coordinate measuring machine (CMM), having a movable measurement probe head within a working volume of the machine.
In a conventional three-dimensional measuring machine, the probe head is supported for movement along three mutually perpendicular axes (in directions X, Y and Z), also referred to as Cartesian configuration with linear axes being more or less orthogonal towards each other.
In a simple form of the machine, a suitable transducer is mounted parallel to each axis and is used to determine the position of the probe head relative to a base of the machine. The coordinates of a measurement point on an object being approached by a probe at the probe head are determined according to the transducer's values. The axis is often driven by a propulsion motor, which is controlled by a dedicated controller, comprising a digital computation unit which moves the axis according to a measurement program or by user input, e.g. by Joystick.
There are several possible sources of error, if such a technique is employed. Lack of straightness in movement and of orthogonality of the axes, lateral offset in the linear drive mechanisms or angular rotation of the carriages about axes perpendicular to their directions of movement, are just a few examples.
Particularly, the following error factors may occur:                scale errors on axes,        horizontal straightness errors on axes,        vertical straightness errors on axes,        pitching errors on axes,        yawing errors on axes,        rolling errors on axes, and        angular errors between axes.        
Many attempts have been made to provide correction for the various sources of error referred to. For example, it is known to introduce a deliberate and known error into the transducers by various means. An alternative technique is to calibrate the machine, measuring the errors existing at various points and storing these, so that they can be compensated when the machine is in measurement use. The execution of such a calibration process is lengthy, especially for a large machine.
A drawback of the calibration methods is also that they will only take care of fully repeatable errors and it is also important to calibrate the probe under the same conditions as in the working state of the machine. This means e.g. that, if the machine runs with 100 mm/sec at measurement, the calibration procedure also should be performed with that speed, and if—for some reason—a change of the running speed is necessary, a recalibration of the machine at this new speed is required, as the errors are at least partly dependent on the dynamics of movement.
The mentioned errors are only analyzed statically in many approaches, although they also comprise dynamic factors which are dependent on the movement of the axes, in particular dependent on the position, speed, acceleration and jerk when moving the axis. With the speed-dependent calibration, this fact is taken into account in a rather simple and inflexible way.
While the static errors can be numerically reduced by the use of position calibration matrices, things get much more complex when trying to compensate the dynamic errors. The calibration gets even more complex when taking into account the dynamic errors, such as vibrations, resonance, dynamic forces, etc. which errors can not only influence the axis on which they are occurring, but which can also “crosstalk” to other axes and cause errors in other parts of the system. Furthermore, the underlying effects can also be dependent on environmental conditions such as temperature, humidity, air-pressure, etc. and in particular, they will also vary over the lifetime of the machine.
Also, an exchange of the probe-head, which is often necessary for fulfilling different measurement tasks on a workpiece, can bring a change of load conditions and result in different dynamics and error behaviour. The usage of probe heads which comprise movable parts and/or additional axes, either active or passive, can result in a different behaviour of the main axis, depending on the actual posture of the probe head. The dynamic behaviour of a machine's axis (as two elements of the machine frame movable relative to each other in a direction of movement) can also vary dependent upon the actual drive position of the axis.
For example, it has to be considered that accelerations of one axis of the machine (which can move further perpendicular axes and the probe head), can cause linear and angular dynamic deflections of the whole frame of the coordinate measuring machine, which in turn cause measurement uncertainties and errors. These dynamic measurement errors may be reduced by taking measurements at low accelerations, e.g. by a consequently optimized trajectory of desired movement.
However, to increase the productivity, an increased throughput as well as an increased inspection speed is demanded. Hence, the machine will experience higher accelerations during the measurements, and larger dynamic structural deflections of the system will result. This leads to an inaccurate reporting of the X, Y, Z geometric position of the probe, resulting in a reduced accuracy or even in incorrect measurements of the workpiece. Those errors are even more severe as CMMs are often required to achieve a measurement accuracy in the range of micrometers or even below.
In particular, a coordinate measuring machine can exhibit drive vibration which can be significant in view of the desired measurement accuracy. The main source of error causing the vibration is the machine's mechanical drive system. The drive vibration is also dependent upon the drive's running speed. Errors caused by these vibrations (typically occurring with a frequency above 5 Hz) are not suitable for calculative methods of compensating dynamic errors as mentioned above, especially as the vibrations are to a great extent non repeatable behaviours, wherefore the resulting measurement errors can not be mathematically modelled and equalized. Also, non-perfect bearings can introduce friction and cause vibrations.
There are passive damping elements known, which introduce a mechanical low-pass or band pass filtering into the mechanical system to reduce vibrations and jerk as far as possible. Those can be integrated parts of the machine, for example by usage of a somewhat “elastic” and “damping” belt in the transmission system or by air or liquid dampers parallel to the axis. Drawbacks of those passive dampers are for example the facts that they can reduce the stiffness of the system, introduce derivation from the desired trajectory of movement by undesired deflection (or displacement) and they can even introduce additional mechanical resonance frequencies.
Other approaches, as e.g. propagated by Convolve Inc. NY, are trying to suppress deflections, vibrations and/or oscillations caused by the acceleration of the machine by a technology called input-shaping, which controls the regulating variable, e.g. the force or current of a propulsion motor, in such a way as to bypass mechanical resonances and avoid a stimulation of resonance frequencies or even actively counterforce oscillations by a accordingly manipulated variable on the output to the driving actuator control.
Also model predictive control, as a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state, can be applied to CMMs. The optimisation yields an optimal control sequence and the first control in the sequence is then applied to the plant.
Furthermore, a variety of probe heads and probes are employed in a coordinate measuring machine for measurements within the scale coordinate system, for example by reference scales arranged along axes, that configure the three-dimensional measuring space. To provide the coordinate measuring machine with an improved measurement precision, its frame structure is therefore required to have a high static stiffness. In order to achieve a stiff and rigid machine design, the frame structure or at least parts of it, is often made of stone, such as granite. Besides all the positive effects like thermal stability and good damping properties, the granite also makes the machine and the movable frame elements quite heavy. The high weight on the other side also requires high forces for a decent acceleration.
In addition to the desirable high frame stiffness, the mentioned introduction of a software implemented spatial precision correction technology can reduce geometrical errors and assist in achieving high precision measurement results.
Another problem in CMM systems lies also in the fact that different probes will have different weights and characteristics, wherefore the machine's mechanical resonance frequencies will be influenced. Also, the spatial position of the machine influences the mechanical resonances, wherefore a simple linear error model is often not sufficient to compensate those influences numerically.
Exemplarily, EP 1 559 990 discloses a coordinate measuring system and method of correcting coordinates measured in a coordinate measuring machine, measuring geometrical errors while parts with various weights are mounted on the coordinate measuring machine. Compensation parameters are derived from measured results per a weight of a part and stored. A compensation parameter corresponding to a weight of a part to be measured is appropriately read out to correct measured coordinates of the part to be measured.
As a further example, EP 1 687 589 discloses a method of error compensation in a coordinate measuring machine with an articulating probe head having a surface detecting device. The surface detecting device is rotated about at least one axis of the articulating probe head during measurement. The method comprises the steps of: determining the stiffness of the whole or part of the apparatus, determining one or more factors which relate to the load applied by the articulating probe head at any particular instant, and determining the measurement error at the surface sensing device caused by the load.
Another approach for error correction of work piece measurements with a coordinate measuring machine (CMM) is disclosed in GB 2 425 840. Thereby, position measurements are taken with a work piece sensing probe, in which means of measuring acceleration are provided. The measurements are corrected for both high frequency (unrepeatable) errors such as those due to vibration, and low frequency (repeatable) errors such as those due to centrifugal forces on the probe. The correction method comprises measuring the work piece, determining repeatable measurement errors from a predetermined error function, error map or error look-up table, measuring acceleration and calculating unrepeatable measurement errors, combining the first and second measurement errors to determine total errors and correcting the work piece measurements using the total errors. The predetermined error map is calculated using an artefact of known dimensions.
It is also known to use accelerometers fitted in the probe or on other moving parts of the measurement machine, e.g. the Z-column and/or in the base table, allowing a differential measurement and/or the evaluation of externally applied vibrations. In such an arrangement, the displacements and errors of the probe-position can be measured with double integration, and based on this information it is possible to adjust the reading with the difference between the doubly integrated signal and the scales.
However, when using accelerometers, the position measurement will usually become noisy, in particular when the frequencies to be measured are relatively low, for example in case of slow and smooth motions. This can result in a bad signal to noise ratio.
Furthermore, it may only be possible to measure differences during acceleration, which means that—in general—it may be necessary to calculate the acceleration from the scale position and to compare it with the measured acceleration, and doubly integrate the difference. However, this may not be enough information to accurately calculate the exact position of the probe. Accelerometer methods can not be used to measure static changes. For example, static friction combined with dynamic changes can not be apprehended by accelerometers.
In particular for large CMMs, shaky environments, and/or if a very high accuracy is required, it is known to build special foundations designed for the erection of measurement machines to achieve a suppression of externally applied vibrations coming from the environment of the measurement machine or to allow a compensation of a possible settling of the machine either coming from the load of the machine itself or from the load of the workpiece to be measured.
Alternatively or in addition to a special foundation, it is also known to set up a CMM using passive or active components for a further decoupling of the measurement machine bed from the ground to avoid or at least reduce influences from external disturbances on the measurement results.
Other related documents are CN 101 562 409, US 2008/100156, DE 196 42 827, US 2009/152985, US 2007/266781, WO 00/14474.
For the propulsion of the machine's axes, there are many different kinds of transmission or drive systems and mechanics known.
An embodiment used quite often comprises a transmission belt, tooth-belt, friction belts, screw, rack and pinion, etc. There needs to be a coupling on the path of transmission of the force between a first frame element with the propulsion unit on one side—and a second frame element, e.g. the probe head, to being moved on the other side. The propulsion unit can be embodied as an electro-mechanical transducer, in particular an electric motor based on magnetic, electrostatic or piezo-active principle. The drive mechanism to achieve the coupling of forces is often designed in such a way that it is stiff in the moving direction and weak in other directions, to allow movement in the other directions without introducing undesired forces in any other direction but the moving direction.
When, for example, a tooth-belt is used, it is relatively easy to avoid forces in the “non moving directions” since the belt as such is flexible, in particular in the directions other than alongside the belt. If a stiffer drive unit such as a screw or rack and pinion is used, then there is a need to have a more sophisticated decoupling of unwanted forces to avoid undesired effects which might reduce accuracy, reproducibility, increase friction, increase wear and/or introduce undesired deformations. There are many mechanical components and arrangements known for achieving such couplings, which are stiff in one degree of freedom only, such as e.g. cardan couplings or gimbals.
In particular when using a belt-drive, there are some disadvantages one of which is the limited stiffness which will result in flexion or distension during acceleration. Furthermore, the limited stiffness can behave like a mechanical resonance circuit which can be modelled by at least one spring—in particular embodied by the elastically behaving tooth-belt—and at least one mass—embodied by the movable member. This will limit the acceleration or force which can be applied to the axis without severe position displacement due to drive mechanism deflection or a stimulation of oscillations. This fact often limits the acceleration profile or force-profile which can practically be applied to the moving member and will also result in at least one mechanical resonance of the system.
A second disadvantage of a toothed belt or another toothed force transmission principle, such as a rack and pinion, are micro vibrations due to the teeth and/or drive wheels. Similar micro vibration can also result from the propulsion motors (also referred to as drive motors) themselves due to effects like torque-ripple (e.g. motor-cogging, oscillations inside the control loop, in particular in cascaded control loops, etc.) or from non-perfect bearings. The vibrations and excitation frequencies to the CMM system in those cases are dependent on the moving speed. Especially when an excitation of a natural frequency of a part of the mechanics occurs, this can lead to an undesired trajectory of movement. In particular, by the high accuracy scales used in such measurement machines, those micro vibrations can often be observed in the measured position or velocity profile of a moving machine, in particular as oscillations overlaid onto the actually desired trajectory profile.